Question

The velocity with which an object should be projected from the surface of the earth such that it reaches a maximum height equal to “n” time the radius of earth “R” is _____ (M = Mass of the earth)

(a) [(n*G*M)/(n+1)R] ^1/2

(b) [((n+1)*G*M)/(n+1)R] ^2

(c) [(n*G*M)/(n+1)R]

(d) [((n+1)*G*M)/nR] ^2

Answer 1

Correct choice is (a) [(n*G*M)/(n+1)R] ^1/2

For explanation I would say: Total initial energy = Total final energy

1/2(m x v^2) – (G*M*m)/R = -(G*M*m)/(n+1)R

Simplifying the above equation, we get;

v = [(n*G*M)/(n+1)R]^1/2